{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "569d620b-882a-4d90-a82a-e0c2bb85de9d",
   "metadata": {},
   "source": [
    "\n",
    "姚端正、周国全、贾俊基《数学物理方法》第四版P.273\n",
    "\n",
    "我们要求解如下的方程，并作出$x,y$ 曲线图\n",
    "$$\n",
    "\\left\\{\\begin{array}{l}\n",
    "x=\\frac{c_1}{2}(\\theta-\\sin \\theta)+c_2 \\\\\n",
    "y=\\frac{c_1}{2}(1-\\cos \\theta)\n",
    "\\end{array}\\right.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e9220533-845d-4da3-88cf-4e204859b2e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *  # 导入sympy 包中所有的函数\n",
    "from sympy.abc import x,y # 引入默认的符号变量\n",
    "c1,c2,theta, n = symbols('c1 c2 theta n') # 自定义符号变量,n是整数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b1db7b4c-a630-474c-8c8a-0e2f2e33cc43",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-acos((c1 - 2*y)/c1) + 2*pi, acos((c1 - 2*y)/c1)]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_expr = c1/2*(1-cos(theta)) -y\n",
    "x_expr = c1/2*(theta - sin(theta)) + c2 -x\n",
    "sols_theta = solve(y_expr, theta) #.simplify() \n",
    "sols_theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "25edbd4e-f5cc-4198-9adc-727b92971e53",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{c_{1} \\left(- \\sqrt{1 - \\frac{\\left(c_{1} - 2 y\\right)^{2}}{c_{1}^{2}}} + \\operatorname{acos}{\\left(\\frac{c_{1} - 2 y}{c_{1}} \\right)}\\right)}{2} + c_{2} - x$"
      ],
      "text/plain": [
       "c1*(-sqrt(1 - (c1 - 2*y)**2/c1**2) + acos((c1 - 2*y)/c1))/2 + c2 - x"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq  =  c1/2*(sols_theta[1]  - sin(sols_theta[1])) + c2 -x  # x，y的表达式\n",
    "eq  # 输出eq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "69f46e53-7489-42ea-988c-46b5bed6d127",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 我们假设曲线过(0,0)和(1,2)点\n",
    "eq1 = eq.subs([(x, 0), (y, 0)])\n",
    "eq2 = eq.subs([(x,1.5), (y, 1)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6df15123-016f-457d-905e-7a81750bf629",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle c_{2}$"
      ],
      "text/plain": [
       "c2"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq1 # 输出eq1，可以看出c2=0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f0920866-bd44-4bc2-98a8-3209a08c0bf3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{c_{1} \\left(- \\sqrt{1 - \\frac{\\left(c_{1} - 2\\right)^{2}}{c_{1}^{2}}} + \\operatorname{acos}{\\left(\\frac{c_{1} - 2}{c_{1}} \\right)}\\right)}{2} + c_{2} - 1.5$"
      ],
      "text/plain": [
       "c1*(-sqrt(1 - (c1 - 2)**2/c1**2) + acos((c1 - 2)/c1))/2 + c2 - 1.5"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq2 # 输出eq2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "800a76b9-5f94-4cde-8489-424dc1759122",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - 1.0 c_{1} \\sqrt{\\frac{c_{1} - 1}{c_{1}^{2}}} + 0.5 c_{1} \\operatorname{acos}{\\left(\\frac{c_{1} - 2}{c_{1}} \\right)} - 1.5$"
      ],
      "text/plain": [
       "-1.0*c1*sqrt((c1 - 1)/c1**2) + 0.5*c1*acos((c1 - 2)/c1) - 1.5"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq2 = eq2.subs(c2, solve(eq1,c2)[0]).simplify() # 把c2的解带入带入eq2，简化eq2\n",
    "eq2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e5277025-d3e6-46a8-9f2c-cde9f5f899d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x21908a504d0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(eq2,(c1,1,1.01) )# ,ylim=(-1,1) ,xlim=(0.8,1.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "495ea182-1db4-4ce0-b477-8c2fc0912ba5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1.00132671190551 - 4.77488298643618 \\cdot 10^{-25} i$"
      ],
      "text/plain": [
       "1.00132671190551 - 4.77488298643618e-25*I"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 求c1的数值,方程为非线性的所以用nsolve函数，设猜测解为 1\n",
    "sols_c1= nsolve(eq2, c1,1.001) \n",
    "sols_c1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "19071805-db55-4ac0-b6d1-99449c30a5e6",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_expr2 = c1/2*(sols_theta[1] - sin(sols_theta[1])) + c2 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "de5a1f7c-c568-49d8-9a61-42411ed5c9dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_expr_1 = x_expr2.subs([(c1, re(sols_c1)),(c2,0)]) # 把c1,c2的值带入表达式"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "26353137-749f-4f00-8fbc-7df8633c1c72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - 1.0 \\sqrt{0.250663795993873 - \\left(0.500663355952753 - y\\right)^{2}} + 0.500663355952753 \\operatorname{acos}{\\left(1.0 - 1.99735009185367 y \\right)}$"
      ],
      "text/plain": [
       "-1.0*sqrt(0.250663795993873 - (0.500663355952753 - y)**2) + 0.500663355952753*acos(1.0 - 1.99735009185367*y)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_expr_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ef5a70d6-6977-406a-bdbd-ccc75cf4836d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = plot(x_expr_1,(y, 0,2),ylabel='x(y)',xlim=(0,2) )# "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a01999c-7670-4fc3-8277-437caf6187c0",
   "metadata": {},
   "source": [
    "如果我们设过 $(0,0)$ 点且$x/y = 1.5$，由前面的分析得$c2 = 0$\n",
    "\n",
    "$$\\frac{x}{y} = \\frac{\\theta - \\sin\\theta}{1-\\cos\\theta} =1.5$$\n",
    "\n",
    "所以我们可以考察这样一个表达式以获取$\\theta$的近似值\n",
    "\n",
    "$$f(\\theta) = 1.5*(1-\\cos \\theta) - \\theta+ \\sin\\theta $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "d8e99924-f215-4774-8843-478babf38df6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AHmNDfpUKKxsUGRKoOSO5Zut4KHEAAMBjtG9ouHB0f4UFW01O49kocQAAwCM0Nrv07pZiSVyzdTIocQAAwCOs2FmqmsYWpcSEKTsz1uw4Ho8SBwAAPMKr6wskSfMnJCuAa7ZOiBIHAABMt6+sVp/nlctika6ZMtDsOF6BEgcAAEz3f2tbR+HOy0pUWmy4yWm8AyUOAACYqr6pRX/fWChJuv6MdJPTeA9KHAAAMNU7OYdU09ii9LhwzRyaYHYcr0GJAwAApjEMQy+tyZckXZ+dzoaGbqDEAQAA02wqqNKOYodCAgN05WTOhusOShwAADBN+yjcZeOTFRMebHIa70KJAwAApiivderfW0skSf91Roa5YbwQJQ4AAJjitfWFanK5NT4tRmNSo82O43UocQAAoM+53IaWr22dSv0vjhU5JZQ4AADQ51bsPKxD9kbFRgRr3tgBZsfxSpQ4AADQ515qG4W7anKaQoOsJqfxTpQ4AADQp468J/W6bO5JPVWUOAAA0Kfa70k9dzj3pJ4OShwAAOgzne5JncaGhtNBiQMAAH3mn0fck3o296SeFkocAADoE4Zh6G/ck9pjKHEAAKBPcE9qz6LEAQCAPtF+T+ql47gntSdQ4gAAQK877Gj85p5UNjT0CEocAADodc+v2qcml1tTMvppbGqM2XF8AiUOAAD0qsq6Ji3/qvVsuAWzhpicxndQ4gAAQK9a9sV+NTS7NDolSmcP41iRnkKJAwAAvcbR2KwXvjwgSVpwzhBZLBwr0lMocQAAoNe8tCZfNY0tGpIYqbmj+psdx6dQ4gAAQK9oaHLpr6v3S5JuP2cwh/v2MEocAADoFa+uL1BFXZPSYsN06bhks+P4HEocAADocU0tbj23ap8k6UdnD1aglcrR0/g3CgAAetybmw6q2N6opKgQfXcSV2z1BkocAADoUS0ut5au3CtJunXGIIUEWk1O5JsocQAAoEe9t7VY+RX16hcepO9lDzQ7js+ixAEAgB7jdhv646eto3C3TM9UeHCgyYl8FyUOAAD0mI93Hlbu4RrZQgJ1w5kZZsfxaZQ4AADQIwzD0LOf7pEk/de0dEWHBZmcyLdR4gAAQI9Yvadcmw/aFRoUoO+flWl2HJ9HiQMAAD3imU9aR+GunTpQcZEhJqfxfZQ4AABw2jYcqNRX+ysVZLXoBzMHmR3HL1DiAADAaXumbS3cdyelakB0mMlp/AMlDgAAnJZtRXZ9llumAIv0w5mDzY7jN07r8Jbm5maVlJSovr5eCQkJio2N7alcAADAS/z2g12SpEvHJSsjPsLkNP6j2yNxNTU1Wrp0qc4++2xFRUUpIyNDI0aMUEJCgtLT03Xrrbdq/fr1vZEVAAB4mJW7y/R5XrmCrBbdN2e42XH8SrdK3FNPPaWMjAwtW7ZMs2fP1ttvv62cnBzt3r1ba9as0cMPP6yWlhbNmTNHF1xwgfLy8norNwAAMJnLbWjxv3dKkm6YlqG02HCTE/kXi2EYxsk+fO211+qXv/ylRo0addznnE6nli1bpuDgYN1yyy2nHfJEHA6HoqOjZbfbFRUV1ev/PAAAIL2+oVA//ccWRYUGatVPZykmPNjsSH6lWyXOU1HiAADoWw1NLp3z5Kc67HDq5xdl6QdsaOhz3ZpOramp0X333dexBm7IkCG66KKLtGjRIu3atau3MgIAAA/z/1bv02GHUykxYbphWobZcfxSt3an3nDDDdq4caNuvfVWJSUlqaGhQT/72c+0b98+PfTQQ7r44ou1dOlSJScn91ZeAABgsvJap/60cp8k6acXDFdokNXkRP6pW9OpERERWr16tSZMmNDxns1m0+bNm2W1WrVo0SK99957Wr16tTIz++7ONKZTAQDoOw+9s01/W5OvMSnRemfBdAUEWMyO5Je6NZ2alJSk+vr6Lj+Xnp6u5557TrfddpvuvvvuHgkHAAA8y76yWr38VYEk6ecXjaDAmahbJe6OO+7QLbfcos2bNx/zmeuvv16ffPLJaQcDAACe57cf7FKL29B5WYmaNjjO7Dh+rVtr4u69914dOnRIEydO1Pnnn6/58+fL7XbLYvmmhb/66quKj4/v8aAAAMBc6w9U6sPthxVgkRZemGV2HL/X7Wu3nnzySV155ZV68skndd9996mhoUHjxo1TfHy87Ha7Ghsb9cILL/RCVAAAYBbDMPRY28G+V09J09Akm8mJcFrnxDU1NWnTpk3avXu3HA6H4uPjde655yoxMbEnM54QGxsAAOhd720p1oKXNyk82KrPfnKOEqNCzY7k97o9Enek4OBgnXHGGTrjjDN6Kg8AAPAwTS1uPfFh63mwt84YRIHzEN3a2FBQUNCtn7yoqKhbzwMAAM/zf2vzlV9RrwRbiH4wc5DZcdCmWyVuypQp+uEPf6j169cf8xm73a7nn39eo0eP1htvvHHaAQEAgHnsDc3630/yJEk/nj1MESGnNYmHHtStr8S8efMUGRmp888/X6GhoZo0aZKSk5MVGhqqqqoq7dixQ9u3b9fEiRP1xBNP6KKLLuqt3AAAoA88+WGuquubNSQxUldNTjU7Do7QrY0NwcHBKiwslM1mU0JCgq699lpVVFSooaFB8fHxmjBhgubOnavRo0f3ZuajsLEBAICel1NYrcv/+IUMQ3r51mydOZgjxDxJt0bikpOTlZOTo7lz56qhoUGPPfZYn+9EBQAAva/F5dYv3toqw5CumJBCgfNA3VoTd9999+mSSy7RjBkzZLFYtHz5cq1fv14NDQ29lQ8AAJjgb2vytf2QQ1Ghgfr5vBFmx0EXulXi7rzzTm3YsEEXXHCBDMPQs88+q2nTpikqKkojRozQNddco8cff1zvv//+KQd6/PHHZbFYdM8995zyzwEAAE5dib1Rv/9PriRp4YUjFB8ZYnIidOWUD/sdOnSo1qxZo4iICG3ZskU5OTkdr23btqmmpqbbP+f69et11VVXKSoqSrNmzdKSJUtO6sexJg4AgJ5z+/KN+vfWEk0YGKM3fnQml9x7qFPeJ5yXl9fx7ezsbGVnZ3d8/1R6YW1tra677jo9//zz+s1vfnOqsQAAwGn4dFep/r21RNYAixbNH0OB82Ddmk49WRZL97/gCxYs0Lx58zR79uwTPut0OuVwODq9AADA6Wlocumhf26TJN0yPUMjk5nd8mQecWLfq6++qk2bNh33EOEjLV68WI8++mgvpwIAwL8882meCisbNCA6VPfMHmZ2HJxAr4zEdUdhYaHuvvtuLV++XKGhJ3cX2wMPPCC73d7xKiws7OWUAAD4trzDNXpu1T5J0iOXjuJmBi9wyhsbesrbb7+tyy+/XFarteM9l8sli8WigIAAOZ3OTp/rChsbAAA4dYZh6Orn1mrd/krNHpGo52+YfEpLo9C3TK/Z5513nrZu3drpvZtvvllZWVn62c9+dsICBwAATs/L6wq0bn+lwoKseuTSURQ4L2F6ibPZbEdd0xUREaG4uLg+v74LAAB/k19Rp0Xv7ZQk3TdnmFL7hZucCCfL9DVxAADAHC63ofte36z6JpeyM2N1y/RMsyOhG0wfievKZ599ZnYEAAB83vOf79OG/CpFhgTqySvHcSacl2EkDgAAP7Sz2KGn/rNbkvTQJSOVFss0qrehxAEA4GecLS79+LUcNbncmj0iSVdOSjU7Ek4BJQ4AAD/z9Md52lVSo9iIYC2+Ygy7Ub0UJQ4AAD+yMb9Sf1q5V5K0aP5oJdhCTE6EU0WJAwDAT9Q3teje1zfLbUhXTEjRhWMGmB0Jp4ESBwCAn1j8713Kr6jXgOhQPXzpKLPj4DRR4gAA8AMrd5fppbX5kqTffXecosOCTE6E00WJAwDAx9nrm/XTf2yWJN04LV1nDY03ORF6AiUOAAAfZhiGfvH2Vh12ODUoPkILLxxhdiT0EEocAAA+7KW1+Xp3S7GsARb9/qpxCgu2mh0JPYQSBwCAj8oprNav390hSVp4QZYmDOxnciL0JEocAAA+qKquSQuWb1Kzy9AFo/rrv2dwub2vocQBAOBj3G5D97yWo6LqBmXEheuJK8dyK4MPosQBAOBjnvl0j1buLlNIYICWXj9JUaEcJ+KLKHEAAPiQz/PK9D8f75Yk/Wb+aI0YEGVyIvQWShwAAD6i2N6gu1/NkWFI10xJ05WT08yOhF5EiQMAwAc0tbi1YPkmVdY1aVRylB7hWi2fR4kDAMAHPP7+Lm0qqJYtNFBLr5uk0CDOg/N1lDgAALzce1uK9dcv9kuSnrpqvAbGhZucCH2BEgcAgBfbU1rTcS/qj84erPNHJpmcCH2FEgcAgJcqr3XqpmXrVdfkUnZmrH4yZ5jZkdCHKHEAAHihxmaXbv3bBh2salB6XLiWXj9JgVb+WvcnfLUBAPAybreh+/6+WV8XVCs6LEh/vWmKYiOCzY6FPkaJAwDAy/z+o1y9t6VYQVaL/nT9JA1OiDQ7EkxAiQMAwIu8vqFQz366V5K0+IqxmjY4zuREMAslDgAAL/Hl3nL9/M2tkqQ7Zg3RdyelmpwIZqLEAQDgBfaU1upHL21Ui9vQxWMH6N7z2Ynq7yhxAAB4uIpap25+YZ0cjS2aODBGT145TgEBFrNjwWSUOAAAPFhjs0s/eGmjCisblBYbpudvmMyVWpBEiQMAwGO53YZ+8vfN2phfJVtooJbdNEVxkSFmx4KHoMQBAOCBDMPQL9/Zpne3FCswwKI/Xz9JQxJtZseCB6HEAQDgYQzD0KL3durlrwpksUhPXT1eZw6JNzsWPAwlDgAAD7Pk4zz9ZfV+SdJvrxirS8clm5wInogSBwCAB3lu1V49vSJPkvTwJSN11ZQ0kxPBU1HiAADwEC+tzddj/94lSbp/7nDdPD3T5ETwZJQ4AAA8wJubDurBt7dJkm4/Z7AWzBpiciJ4OkocAAAme39rsX7y982SpJvOzND9c4ebnAjegBIHAICJPs0t1V2vfi23IV05KVUPXTxSFgu3MeDEKHEAAJhk7b4K/eiljWp2td6H+vh3xnKdFk5aoNkBAADwR1/uKdd//22DnC1uzR6RqP+5erysFDh0AyUOAIA+9smuw/rR/21SU4tbM4bG65nvTVSQlckxdA8lDgCAPvTelmLd/erXanEbOn9kkp753gSFBHKhPbqPEgcAQB95fUOhFr6xRW5Dumx8sp68chwjcDhllDgAAPrAi18e0MP/3C5JumZKmhZdPoY1cDgtlDgAAHrZHz/boyc+yJUk3TI9Uw9ePIJjRHDaKHEAAPQSwzD0+//s1jOf7pEk3XXuEP34/GEUOPQIShwAAL3A7Tb06/d2aNkXByRJCy/M0o/OHmxuKPgUShwAAD2ssdmln/x9s97dUixJ+vVlo/Rf0zLMDQWfQ4kDAKAHVdQ69YOXNmpjfpUCAyx64rtjdcXEVLNjwQdR4gAA6CF7y2p1ywvrlV9Rr6jQQP3p+kk6c0i82bHgoyhxAAD0gLX7KvTDlzbK3tCstNgwLbtpioYk2syOBR9GiQMA4DS9uemgfvbGFjW7DE0YGKPnb5is+MgQs2PBx1HiAAA4RYZhaMnHeXp6RZ4kad6YAfr9VeMUGsQ1Wuh9lDgAAE6Bs8WlhW9s1VtfF0mSbjtnsO6fM1wB3MKAPkKJAwCgm6rrm/SDlzZq3f5KWQMsWjR/tK6ZOtDsWPAzlDgAALphb1mtbn1xg/aV18kWEqg/Xj9RM4YmmB0LfogSBwDASXp/a7Hu/8cW1TpblBITpr/eNEXD+7MDFeagxAEAcAItLree+DBXz63aJ0nKzozVH743QYm2UJOTwZ9R4gAAOI6yGqfufGWT1u6rlCT9YOYg/XTucAVaA0xOBn9HiQMA4Bg2HKjU7cs3qbTGqciQQP3uu2N14ZgBZscCJFHiAAA4imEYWvbFAT32751qcRsamhipP/3XJA1OiDQ7GtCBEgcAwBHqnC1a+OZW/WvzIUnSJeOS9fgVYxQRwl+Z8Cz8jgQAoM2e0hrd9n+blFdaq8AAi34xb4RuOjNDFgsH+MLzUOIAAH7PMAy9sq5Qv3p3uxqb3UqKCtGz35uoyRmxZkcDjokSBwDwa9X1TVr4xlZ9sL1EkjRjaLx+f9U4jg+Bx6PEAQD81pq9FfrxazkqcTQqyGrRT+dm6ftnZXL/KbwCJQ4A4HeaXW49/XGenv1sjwxDyoyP0P9eM0FjUqPNjgacNEocAMCv7D5co3tfz9G2Iock6arJqXr4klHsPoXX4XcsAMAvuNyG/vL5Pv3+P7vV5HIrOixIiy4frYvHJpsdDTgllDgAgM/bX16nn/x9szbmV0mSzs1K1ONXjFFiFJsX4L0ocQAAn+V2G3ppbb4Wv79Tjc1uRYYE6qFLRurKSamc/QavR4kDAPik/eV1euDNLR0X108fEqfffmesUvuFm5wM6BmUOACAT2l2ufXcqn16ekWemlrcCguy6oGLsnR9djpHh8CnUOIAAD4jp7BaC9/Yol0lNZJaD+597PIxSotl9A2+hxIHAPB6dc4WPfmfXL345QG5DalfeJAeumSk5o9PYe0bfBYlDgDgtQzD0Mc7S/XIP7erqLpBknT5hBT9ct4IxUWGmJwO6F2UOACAV8qvqNMj/9yuT3PLJEkpMWF67IoxOntYgsnJgL5BiQMAeJWGJpeWfrZHf1q1T00tbgVZLfr+WYN057lDuHUBfiXA7ACStHjxYk2ZMkU2m02JiYmaP3++cnNzzY4FAPAghmHoP9tLdP7/rNT/frJHTS1uzRgarw/umamFF2ZR4OB3POJ3/MqVK7VgwQJNmTJFLS0t+vnPf645c+Zox44dioiIMDseAMBk+8pq9et3d3RMnSZHh+qXF4/UhaP7s3EBfstiGIZhdohvKysrU2JiolauXKmZM2ee8HmHw6Ho6GjZ7XZFRUX1QUIAQF+orm/S0yvy9NKafLW4DQVZLbp1xiDdce4QhQd7xDgEYBqP/C/AbrdLkmJjY7v8vNPplNPp7Pi+w+Hok1wAgL7R7HLrpTX5enpFnuwNzZJa7zv9xbwRGpwQaXI6wDN43Eic2+3WpZdequrqaq1evbrLZx555BE9+uijR73PSBwAeLf2I0MW/3un9pXXSZKy+tv0i3kjNGMou06BI3lcibvtttv0/vvva/Xq1UpNTe3yma5G4tLS0ihxAODFthys1uPv79KXeyskSfGRwbpvznBdNTlNVq7LAo7iUdOpd9xxh959912tWrXqmAVOkkJCQhQSwiGOAOAL9pbV6vf/ydW/t5ZIkoIDA/TfZ2XqtnMGyxYaZHI6wHN5RIkzDEN33nmn3nrrLX322WfKzMw0OxIAoJcV2xv09Md5+vvGg3K5DVksrbct/Hj2MO46BU6CR5S4BQsW6OWXX9Y777wjm82mkpLW/xuLjo5WWFiYyekAAD2pqq5JS1fu1QtfHlBTi1uSNHtEku6fO1zD+9tMTgd4D49YE3esM36WLVumm2666YQ/niNGAMDz2eub9f9W79OyLw6oxtkiSZqaGaufXTBck9K7Po0AwLF5xEicB/RIAEAv6aq8jRwQpZ9eMFxnD0vgsF7gFHlEiQMA+J6uyltWf5vumT1Uc0b2VwA7ToHTQokDAPQoyhvQNyhxAIAecdjRqL+u3q/lXxWolvIG9DpKHADgtOwvr9Nzq/bqjY1FanK17jalvAG9jxIHADgl24rsWrpyr97fWix32/60yen9dPuswZo1PJENC0Avo8QBAE6aYRj6Yk+F/rxqrz7PK+94/9ysRN12zmBNyeCoEKCvUOIAACfkbHHpnZxD+uvq/dpVUiNJsgZYdMnYAfrh2YM1YgBndAJ9jRIHADimilqnln9VoL+tyVd5rVOSFB5s1ZWTUvX9swZpYBzXYwFmocQBAI6SW1KjF748oDc3HZSz7WqsAdGhuvHMDF07ZaCiw7mYHjAbJQ4AIElqdrn10Y7DevHLA/pqf2XH+2NTo/X9szJ10ZgBCrIGmJgQwJEocQDg50prGvXqukIt/ypfhx2tU6bWAIvmjEzSzdMzNSWjHztNAQ9EiQMAP2QYhjbmV+lva/L1/rZiNbtazwiJjwzWtVMH6nvZAzUgOszklACOhxIHAH7EXt+sN78+qFfWFWj34dqO9ycOjNGNZ2bogtH9FRJoNTEhgJNFiQMAH2cYhjbkV+mVrwr03tbijo0KoUEBumRssm48M0OjU6JNTgmguyhxAOCjKuua9NbXRXplXYH2lH4z6pbV36bvZQ/UZeNTFB3GLlPAW1HiAMCHNLvcWplbpn9sPKgVuw53rHULC7Lq0nHJujZ7oMalRrNRAfABlDgA8AG7Shz6x4aDejunSOW1TR3vj0mJ1jVT03TpuGTZQhl1A3wJJQ4AvFRlXZP+mVOkf2w6qG1Fjo734yODdfmEFH1nUqqy+nMdFuCrKHEA4EUam11asbNU7+QU6dPc0o7p0iCrRedlJenKyamaOSyBQ3kBP0CJAwAP53Ib+nJvud7JOaQPtpWo1tnS8bnRKVH67sRUXTo+RbERwSamBNDXKHEA4IEMw9CWg3a9k3NI/9pySGU1zo7PpcSE6dLxybpsfDLTpYAfo8QBgIcwDEO7Smr03pZivbvlkA5U1Hd8LiY8SPPGDND8CSmaNLCfAgLYXQr4O0ocAJhs9+EavdtW3PaV1XW8HxoUoPNH9tf88cmaMTRBwYGscwPwDUocAPQxwzCUe7hGH2wr0b+3Fne6/io4MECzhido3thknZeVqIgQ/pgG0DX+dACAPmAYhrYW2fX+thJ9sK1E+8u/GXELtgZo5rAEXTx2gM4bkch5bgBOCiUOAHpJi8ut9Qeq9NGOw/pwe4mKqhs6PhccGKCZQxN0wej+On9kEtdfAeg2ShwA9KCGJpdW5ZXpP9sPa8Wuw6qub+74XHiwVbOGJ+qC0f01KytRkUyVAjgN/AkCAKep1NGoT3NL9fHOUn2eV6bGZnfH5/qFB+m8EUk6f2SSzh6WoNAgq4lJAfgSShwAdJPbbWjbIbtW7CzVJ7tKtbXI3unzqf3CNGdkf80ZlaTJ6f0UyO0JAHoBJQ4ATkKts0Wr88r1ya7D+jS3rNPhu5I0Li1G5w5P1JxRScrqb5PFwjluAHoXJQ4AumAYhvaV12llbpk+zS3VV/sq1eT6Zpo0ItiqmcMSdG5Wos4ZnqgEW4iJaQH4I0ocALSpaWzWl3srtGp3mVbuLtPBqoZOn0+PC9d5WUk6NytRUzNjOXwXgKkocQD8ltttaEexQyt3l2nV7jJtzK9Si9vo+HywNUBTM2N19rAEnTsiUYPiI5gmBeAxKHEA/Mqh6gat3lOuL9pe5bVNnT6fGR+hs4cl6OxhCcoeFKvwYP6YBOCZ+NMJgE9zNDZr7d4Krd5TrtV7yjvdTSq1nt125uB4nT0sXjOHJSg9LsKkpADQPZQ4AD6lsdmlTflVWrOvQl/sKdfmg3a5jpgiDbC07iQ9a0i8zhoSrwkD+7G2DYBXosQB8GpNLW7lFFZrzd4KrdlXrk0F1WpqcXd6ZlB8hKYPiddZQ+N1xqA4rrgC4BMocQC8SlOLW1sOVuur/ZVau69CGw5UqaHZ1emZpKgQTRsUp2mD4zR9SLxS+4WblBYAeg8lDoBHa2x2KaewWl/tq9RX+yu0qaCq07VWkhQXEawzBsd1FDd2kQLwB5Q4AB6l1tmiTflVWn+gUl/tr1RO4dHTo7ERwZqaEavsQbE6c3C8hiVFUtoA+B1KHABTldY0asOB1tK2/kCldhxy6Ih9CJKkBFuIsjNjW1+D4jQkIVIBAZQ2AP6NEgegz7jdhvaU1WpjfpU2HKjSxvxKHaioP+q5tNgwTcmI1ZSM1uKWyfQoAByFEgeg19Q5W7S5sFob86u0saBKm/Kr5Ghs6fSMxSJl9Y/S1Ix+mtxW3PpHh5qUGAC8ByUOQI8wDEMHKur1dUGVNhVU6euCau0qqel0RpskhQVZNT4tRpMz+mliej9NHNiPIz8A4BRQ4gCcEkdjs7YU2vV1QZW+LqzW1wVVqqpvPuq55OhQTcqI1aSBMZqcEaus/jYFWjlcFwBOFyUOwAk1tbi1q8ShzYXV+rqwWpsLq7X3W9dXSa0Xxo9OidKEga0jbBMGxig5JsyExADg+yhxADoxDEP5FfXKKaxWTmG1Nh+s1vZDjqOO+ZCk1H5hGp8W01HYRiZHKSTQakJqAPA/lDjAjxmGoUP2Rm09WK0tB+3aWmTXloN22RuOnhaNDgvSuLQYjU+L0fi0aI1NjVF8ZIgJqQEAEiUO8CuHHY2tZe1gtbYU2bX1oF0VdU1HPRccGKBRyVEalxqjCQNjNC41Rulx4RzzAQAehBIH+KD2EbZtRXZtL7Jr2yGHthXZVVrjPOrZwACLhiXZNC4tWmNSYjQmJVrD+9sUHMjmAwDwZJQ4wMu53YYKq+q1rcihbYfsrcXtkEOVXYywBVikoYk2jUmN1tjUaI1JidaIAVEKDWIdGwB4G0oc4EWaWtzKK63R9kMO7Wh77Sx2qMbZctSzgQEWDU2yaXRylEanRGt0SpRGDIhSeDD/2QOAL+BPc8BD2RuatbO4taS1l7a80ho1u4yjng22BihrgE2jklvL2ujk1ilRRtgAwHdR4gCTud2GCirrOwrbjuIa7Sx2qKi6ocvno0IDNTI5SqOSozVyQJRGpURpcEKkgjhAFwD8CiUO6EOOxmbtLqnRzpIa7WorbbklNaprcnX5fEpMmEYMsGlke2FLjlJqvzB2iQIAKHFAb2hxuXWgok47i2u0q6S1qO0srjnm6FpwYICGJ9k0YoBNIwa0rl0b0T9K0eHcKQoA6BolDjgN7Ud57C6pUe7hGuWWtL72lNV2ecOBJA2IDtXw/jYN72/TyAFRGjkgSpnxEdwnCgDoFkoccJLKa53afbhGeYdrtaukRrsP12h3SU2XO0MlKTzYquH9bcrqH6Ws/ra2F6NrAICeQYkDvqW6vkm7D9e2lrS2V97h2i5vNpBaj/IYnBCpYf1tGp4UqeH9ozQsKVJp/cIVEMDaNQBA76DEwW9V1TUpr7S1rO0prVVeaWtZ6+pWA0myWKS0fuEalhSp4f1tGpbUOrKWGR/B7QYAgD5HiYNPMwxD5bVN2lNaqz2lNdp9uLWs7SmtVXlt1yNrUuuu0GFJkRqWZNPQJJuGJ9k0JDFSYcGcuwYA8AyUOPgEt9tQUXWD9pTVam9pbVtpq1Veaa3sDc3H/HGp/cI0NDFSQ5NsHR8HJ0TIFsq6NQCAZ6PEwas0tbiVX1GnPaW12lvWVtbKarW3tE4NzV2ftXbkNOiQxNayNizJpsGJEVxBBQDwWvwNBo9kr2/W3vLajrK2t7ROe8tqVVBZL5f76GunJCnIalFmfISGJto0ODFSQxIjNSQhUoMSIrh+CgDgcyhxME2Ly62DVQ3aV95a0o78eLz1apEhgRqcGKnBCREanBCpoW2FbWBsOGetAQD8BiUOva66vkl7y+q0r6xW+8rbPpbVKb+iXk2urg/ElaT+UaEanBihIQmRrSNrbR8TbSFcOwUA8HuUOPQIZ4tLBRX12ltWp/1tRW1/eZ32ldep8hjnq0lSSGCAMuMjWkfW2j4Oio9UZkKEIkP47QkAwLHwtyROmtttqNjRqP1lddpf3j6q1lraDlbV6xhL1SS1jqoNSohofcW3rlMbnBCplJgwDsQFAOAUUOLQiWEYqqhr0v7yuo7XgSO+7TzGfaBS61q1QQkRyoyP6BhNGxTf+v0IRtUAAOhR/M3qp+wNzZ3K2f7yOh2oqNP+srpj3gUqte4AHRgbrsy20bTWwhahzIQIJUSyVg0AgL5CifNhtc6WjqJ2oLxO+ytaPx6oqD/uOjWLRUqODlNmfIQy4sM7jaqlxISxAxQAAA9AifNydc4WHaio04Hy+raPbSNq5fUqr+36DtB2CbaQjpG0jPgIZcS1rlkbGBvOuWoAAHg4SpwXqHW2KP9bRS2/ol77K+pUdozL2tvFRQR3FLTM+PCOb2fEs/sTAABvxt/iHsLR2Kz8tpKWX9E65dk+9XmiEbXYiGClx4UrMy5C6XGtU6CZbaNrUdwBCgCAT6LE9RHDMFRd39xW0uqP+ni8NWqS1C88SBnxEUcVtfS4CEWHUdQAAPA3lLgeZBiGymqdyq+ob3u1jqTlt02BOhqPvetTkuIjQ5QR1z7lGd5a1uIiNDAunKIGAAA6ocR1k8ttqNjeoIKK+o6C1j6iVlBZr/om13F/fP+oUKXHhSsjLkLp8a0fB8aGs0YNAAB0C62hC00tbh2sqld+Zb3yy+taP7YVtsLKhuPe9xlgkZJjwjqKWkZcROu34yOU1i9cYcHs+gQAAKfPo0rcs88+q9/97ncqKSnRuHHj9Ic//EFTp07tlX9WfVOLCirrdaC8XgWVrdOeBW0jaoeqG457hVSQ1aK02HClx7ZPebZ+TI8LV2q/cAUHco4aAADoXR5T4l577TXde++9+tOf/qTs7GwtWbJEc+fOVW5urhITE0/p56yub+qY8myf/mwvbCc6miMsyKr0uPCOEbWBcd9MfSbHhMnKfZ8AAMBEFsMwjjPm1Heys7M1ZcoUPfPMM5Ikt9uttLQ03XnnnVq4cOFxf+xnWw9o1thM/eqN9SppDFBBW3E70UaCmPCgjtG09LjwjrVp6XHhXCEFAAA8Wq+NxBmGoZqampN6tqmpSRs2bNDdd98th8PR8f7MmTO1atUq3X777Z2edzqdcjq/GUn72StfSZL+/PF2BYSEd3o20RastH4RSo0N08DY1qKWFhumtH4Rig4/xo5Po0k1Ncc/8gMAAKA32Wy24w4o9dpInMPhUHR0dG/81AAAAD7PbrcrKirqmJ/vtRLXnZG44uJiZWVl6aOPPuq0keHBBx/UF198oU8++aTT898eiSsuLtbUqVO1Y8cOpaSk9MwvAL3C4XAoLS1NhYWFx/2NCfPxtfIufL28B18r72H21+pEI3G9Np1qsVhO+hccGhoqq9Wq2traTj+murpaKSkpJ/3z2Gw2/oPwElFRUXytvARfK+/C18t78LXyHp76tfKIszCCg4M1adIkrVixouM9t9utFStWaNq0aSYmAwAA8Ewec8TIvffeqxtvvFGTJ0/W1KlTtWTJEtXV1enmm282OxoAAIDH8ZgSd/XVV6usrEwPPfSQSkpKNH78eH3wwQdKSko64Y8NCQnp9BGeKyQkRA8//DBfKy/A18q78PXyHnytvIenf6085py409G+E/ZEuzgAAAB8hUesiQMAAED3UOIAAAC8ECUOAADAC1HiAAAAvJBPlLjnnntOkpSQkKDs7GytW7fO5ET4tlWrVumSSy5RcnKyLBaL3n77bbMj4RgWL16sKVOmyGazKTExUfPnz1dubq7ZsdCFpUuXauzYsR0HkU6bNk3vv/++2bFwEh5//HFZLBbdc889ZkdBFx555BFZLJZOr6ysLLNjHcXrS9xrr72mn//855Kkzz//XOPGjdPcuXNVWlpqcjIcqa6uTuPGjdOzzz5rdhScwMqVK7VgwQKtXbtWH330kZqbmzVnzhzV1dWZHQ3fkpqaqscff1wbN27Uhg0bdO655+qyyy7T9u3bzY6G41i/fr3+/Oc/a+zYsWZHwXGMGjVKxcXFHa/Vq1ebHekoXn/ESHZ2tsaNG6fnn39edrtdkZGRSktL05133qmFCxeaHQ9dsFgseuuttzR//nyzo+AklJWVKTExUStXrtTMmTPNjoMTiI2N1e9+9zt9//vfNzsKulBbW6uJEyfqj3/8o37zm99o/PjxWrJkidmx8C2PPPKI3n77beXk5Jgd5bi8eiSuqalJGzdu1DnnnNPxXkBAgGbPnq01a9aYFwzwIXa7XVJrOYDncrlcevXVV1VXV8d1hR5swYIFmjdvnmbPnm12FJxAXl6ekpOTNWjQIF133XUqKCgwO9JRPObGhlNRXl4ul8ulxMTETu8nJSVp165dJqUCfIfb7dY999yj6dOna/To0WbHQRe2bt2qadOmqbGxUZGRkXrrrbc0cuRIs2OhC6+++qo2bdqk9evXmx0FJ5Cdna0XXnhBw4cPV3FxsR599FHNmDFD27Ztk81mMzteB68ucQB614IFC7Rt2zaPXAuCVsOHD1dOTo7sdrv+8Y9/6MYbb9TKlSspch6msLBQd999tz766COFhoaaHQcncOGFF3Z8e+zYscrOzlZ6erpef/11j1qq4NUlLj4+Xlar9ahNDIcPH1b//v1NSgX4hjvuuEPvvvuuVq1apdTUVLPj4BiCg4M1ZMgQSdKkSZO0fv16Pf300/rzn/9scjIcaePGjSotLdXEiRM73nO5XFq1apWeeeYZOZ1OWa1WExPieGJiYjRs2DDt2bPH7CidePWauODgYE2aNEkrV67seM/tdmvFihWsCQFOkWEYuuOOO/TWW2/pk08+UWZmptmR0A1ut1tOp9PsGPiW8847T1u3blVOTk7Ha/LkybruuuuUk5NDgfNwtbW12rt3rwYMGGB2lE68eiROku69917dcMMNkqTc3Fz95S9/UV1dnW6++WaTk+FItbW1nf4PZv/+/crJyVFsbKwGDhxoYjJ824IFC/Tyyy/rnXfekc1mU0lJiSQpOjpaYWFhJqfDkR544AFdeOGFGjhwoGpqavTyyy/rs88+04cffmh2NHyLzWY7al1pRESE4uLiWG/qgX7yk5/okksuUXp6ug4dOqSHH35YVqtV1157rdnROvH6Enf11VertLRUTzzxhKZPn64JEybogw8+UFJSktnRcIQNGzZo1qxZHd+/9957JUk33nijXnjhBZNSoStLly6VpE67viVp2bJluummm/o+EI6ptLRUN9xwg4qLixUdHa2xY8fqww8/1Pnnn292NMCrHTx4UNdee60qKiqUkJCgs846S2vXrlVCQoLZ0Trx+nPiAAAA/JFXr4kDAADwV5Q4AAAAL0SJAwAA8EKUOAAAAC9EiQMAAPBClDgAAAAvRIkDAADwQpQ4AAAAL0SJAwAA8EKUOAB+xTAMPfXUU8rMzFR4eLjmz58vu91udiwA6DZKHAC/cv/992vp0qV68cUX9fnnn2vjxo165JFHzI4FAN3G3akA/MZXX32ladOmacOGDZo4caIk6Ve/+pWWL1+u3Nxck9MBQPcwEgfAbzz55JM677zzOgqcJCUlJam8vNzEVABwaihxAPyC0+nUe++9p8svv7zT+42NjYqOjjYpFQCcOqZTAfiFNWvW6Mwzz1RoaKisVmvH+83NzZo1a5Y++OADE9MBQPcFmh0AAPrC7t27FRERoZycnE7vz5s3T9OnTzcnFACcBkocAL/gcDgUHx+vIUOGdLyXn5+vvLw8fec73zExGQCcGtbEAfAL8fHxstvtOnIFyaJFi3TRRRdp5MiRJiYDgFPDSBwAv3DuueeqsbFRjz/+uK655hotX75c//rXv7Ru3TqzowHAKWEkDoBfSEpK0gsvvKClS5dq1KhRWrt2rVavXq20tDSzowHAKWF3KgAAgBdiJA4AAMALUeIAAAC8ECUOAADAC1HiAAAAvBAlDgAAwAtR4gAAALwQJQ4AAMALUeIAAAC8ECUOAADAC1HiAAAAvBAlDgAAwAv9f8Ea39AGlQ6dAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x2191bc0b690>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr_xdy =  (theta - sin(theta))/(1-cos (theta) )\n",
    "plot(expr_xdy,(theta, 0,1.6*pi))#,ylabel='x(y)',xlim=(0,2) )# "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4e6a8ced-b14b-4ac8-a14c-c36dd397ddff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x2191be9af90>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_theta  = 1.5*(1-cos (theta) )- theta + sin(theta)\n",
    "plot(f_theta,(theta, 0,2*pi))#,ylabel='x(y)',xlim=(0,2) )# "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "82be782c-1716-4e26-a51d-7dd1bce0a412",
   "metadata": {},
   "outputs": [],
   "source": [
    "sols_theta2 = nsolve(f_theta, theta,4) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "4eb4e1ee-595a-421e-a3c9-21ce964b0f0f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 3.06877673074911$"
      ],
      "text/plain": [
       "3.06877673074911"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sols_theta2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "2d2ed5e1-2426-42c5-a093-08739e4c8b00",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1.99735009185367$"
      ],
      "text/plain": [
       "1.99735009185367"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1-cos (sols_theta2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "82a5b352-e7b8-469a-9b02-6b9bf43e1235",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2.99602513778051$"
      ],
      "text/plain": [
       "2.99602513778051"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sols_theta2 - sin(sols_theta2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "5f83dcf9-72c9-408c-97f1-6b0f47fc62ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1.00132671190551$"
      ],
      "text/plain": [
       "1.00132671190551"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3/(sols_theta2 - sin(sols_theta2)) # 这就是c1的值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "7a16f2c3-e845-40a2-b601-a9e4a320e2ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_expr_2 = x_expr2.subs([(c1, re(sols_c1)),(c2,0)]) # 把c1,c2的值带入表达式\n",
    "x_expr_2 = x_expr_2.subs(c1, re(6/(sols_theta2 - sin(sols_theta2)))) # 把c1,c2的值带入表达式"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "961c742e-de77-454f-a3df-6a58a945bed2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - 1.0 \\sqrt{0.250663795993873 - \\left(0.500663355952753 - y\\right)^{2}} + 0.500663355952753 \\operatorname{acos}{\\left(1.0 - 1.99735009185367 y \\right)}$"
      ],
      "text/plain": [
       "-1.0*sqrt(0.250663795993873 - (0.500663355952753 - y)**2) + 0.500663355952753*acos(1.0 - 1.99735009185367*y)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_expr_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "cc16b6f4-c384-4d3a-8bf0-0f6405da7294",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x2191bc6e250>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(x_expr_2,(y, 0,1),ylabel='x(y)' )# "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ec28dbdb-4cd0-45c8-9b87-8b352ff97a5b",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
